Electronic Communications in Probability

Concentration inequalities via Malliavin calculus with applications

John Treilhard and Abdol-Reza Mansouri

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We use the Malliavin calculus to prove a new abstract concentration inequality result for zero mean, Malliavin differentiable random variables which admit densities. We demonstrate the applicability of the result by deriving two new concrete concentration inequalities, one relating to an integral functional of a fractional Brownian motion process, and the other relating to the centered maximum of a finite sum of Normal random variables. These concentration inequalities are, to the best of our knowledge, largely unattainable via existing methods other than those which are the subject of this paper.

Article information

Electron. Commun. Probab., Volume 20 (2015), paper no. 36, 14 pp.

Accepted: 8 May 2015
First available in Project Euclid: 7 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60H07: Stochastic calculus of variations and the Malliavin calculus
Secondary: 60G22: Fractional processes, including fractional Brownian motion

Malliavin calculus concentration inequalities fractional Brownian motion

This work is licensed under a Creative Commons Attribution 3.0 License.


Treilhard, John; Mansouri, Abdol-Reza. Concentration inequalities via Malliavin calculus with applications. Electron. Commun. Probab. 20 (2015), paper no. 36, 14 pp. doi:10.1214/ECP.v20-3931. https://projecteuclid.org/euclid.ecp/1465320963

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